Running is the easiest sport to get into, the cheapest activity to do, and the most frustrating or exhilarating, depending on how you roll. Whatever type of running you end up doing, here are some recommendations for you.
Lightweight merino wool or cotton baselayer. Baselayers are the tops closest to your skin.
Shorts. Wicking. Spandex, cotton are OK great.
Minimalist OR max-cushioned running sneakers.
Light cotton socks and/or compression socks.
Bandana (it's multi-purpose and always useful).